Question

describe the key features of a parabola with the equation $x^2 = 40y$. the value of $p$ is \\(\boldsymbol{\checkmark}\\). the parabola ope \\(\boldsymbol{\checkmark}\\). the coordinates focus are \\(\boldsymbol{\checkmark}\\). the equation for rectrix is \\(\boldsymbol{\checkmark}\\).

Explanation:

Step1: Recall the standard form of a parabola

The standard form of a parabola that opens up or down is \(x^{2}=4py\), where \(p\) is the distance from the vertex to the focus (and also from the vertex to the directrix).

Step2: Compare with the given equation

Given the equation \(x^{2} = 40y\), we compare it with \(x^{2}=4py\). So, \(4p=40\).

Step3: Solve for \(p\)

To find \(p\), we divide both sides of the equation \(4p = 40\) by 4: \(p=\frac{40}{4}=10\).

Answer:

10